Subgroups — D₃×#401 #78429

Order 384.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#95	C₂	1	7	yes	maximal
3	C₃⋊#401	C₂	1	7	yes	maximal, complemented
4	C₂×#401	—	3	1	no	maximal, Sylow
5	C₂²×C₄×D₃	C₂²	1	7	yes	—
6	C₃×#95	C₂²	1	7	yes	—
7	C₃⋊#95	C₂²	1	21	yes	—
8	#401	—	3	7	no	—
9	#401	D₃	1	1	yes	characteristic, direct product factor
10	C₂×#95	—	3	7	no	—
11	C₂³×D₃	C₂³	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₂³	1	7	yes	—
13	C₂²×Dic₃	C₂³	1	7	yes	—
14	C₂×C₄×D₃	—	2	42	no	—
15	C₂³×C₄	—	3	7	no	—
16	#95	—	3	21	no	—
17	#95	C₂×D₃	1	7	yes	—
18	C₂³×C₃	C₂⁴	1	1	yes	characteristic
19	C₂²×D₃	#41	1	14	yes	—
20	C₂×C₃×C₄	—	2	21	no	—
21	C₂×Dic₃	—	2	21	no	—
22	C₄×D₃	—	4	28	no	—
23	C₂⁴	—	3	1	no	—
24	C₂²×C₄	—	3	7	no	—
25	C₂²×C₄	—	6	42	no	—
26	C₂²×C₄	C₂²×D₃	1	7	yes	—
27	C₂²×C₃	C₂×#41	1	7	yes	—
28	C₂×D₃	#126	1	28	yes	—
29	C₃×C₄	—	4	7	no	—
30	Dic₃	—	4	7	no	—
31	C₂³	—	3	14	no	—
32	C₂³	C₂³×D₃	1	1	yes	characteristic
33	C₂×C₄	—	2	21	no	—
34	C₂×C₄	—	6	21	no	—
35	C₂×C₄	—	12	28	no	—
36	C₂×C₃	C₂×#126	1	7	yes	—
37	D₃	#401	1	8	yes	direct product factor
38	C₂²	—	3	28	no	—
39	C₂²	D₃×#41	1	7	yes	—
40	C₄	—	4	7	no	—
41	C₄	—	12	7	no	—
42	C₃	C₂×#401	1	1	yes	characteristic, complemented, Sylow
43	C₂	—	3	8	no	—
44	C₂	D₃×#126	1	7	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.